That was only his third start in nine games for the Reds this season, having been demoted to a squad role following his stint as first-choice left-back last term.
And as Liverpool prepare to take on Tottenham at Wembley on Sunday afternoon, Klopp was coy over whether Milner would be retained.
“I was never in doubt about Milly, nothing new,” he told reporters, diplomatically.
“I’m really happy for him, that he performed that well—like all the others, thank god!
“But that’s the situation we wanted to have, the situation we need to have: to have more highest-quality players than 11.
“I respect Milly a lot, a very important player for us on the pitch and off the pitch. No problems with that, good.”
If Henderson does return to the fold at the weekend, taking over from Milner, it will likely cause a stir among some supporters.
The captain has been in questionable form so far this season, finding himself under scrutiny for his ability to shield Liverpool’s under-fire back line.
But Klopp insisted that Henderson was only omitted from the lineup at Maribor to manage his fitness, with a return set for Sunday.
“I never speak about the lineup, but Jordan is our skipper. I thought it made sense [to rest him],” he said.
“He had both international games with England, 90 minutes—I wasn’t very happy about this—then played the next game against United, a very intense game for a defensive midfielder.
“It was clear we’d make one change in this game and it was Jordan, but that’s all.”
The suggestion that Henderson should keep his place in the side purely because he was given the captaincy by Brendan Rodgers two years is a problematic one.
But by the same token, to leave him out following one standout performance from Milner could be considered a knee-jerk reaction—though it is clear the vice-captain deserves more minutes.